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HOLOSYMMETRIC CLASS (Holohedral (ass,...

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Originally appearing in Volume V07, Page 575 of the 1911 Encyclopedia Britannica.
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HOLOSYMMETRIC CLASS (Holohedral (ass, whole) ; Hexakis-octahedral). Crystals of this class possess the full number of elements of symmetry already mentioned above for the octahedron and the cube,. viz. three cubic planes of symmetry, six dodecahedral planes, three tetrad axes of symmetry, four triad axes, six dyad axes, and a centre of symmetry. There are seven kinds of simple forms, viz. : Cube (fig. 5). This is bounded by six square faces parallel to the cubic planes of symmetry; it is known also as the hexahedron. The angles between the faces are 90°, and the indices of the form are {too}. Salt, fluorspar and galena crystallize in simple cubes. Octahedron (fig. 3). Bounded by eight equilateral triangular faces perpendicular to the triad axes of symmetry. The angles between the faces are 70° 32' and too° 28', and the indices are 11111. Spinel, magnetite and gold crystallize in simple octahedra. Combinations. of the cube and octahedron are shown in figs. 6-8. Rhombic dodecahedron (fig. 13). Bounded by twelve rhombshaped faces parallel to the six dodecahedral planes of symmetry. The angles between the normals to adjacent faces are 6o°, andbetween other pairs of faces 9o°; the indices are {1Io}. Garnet frequently crystallizes in this form. Fig.. 14 shows the rhombic dodecahedron in combination with the octahedron. In these three simple forms of the cubic system (which are shown in combination in fig. I I) the angles between the faces and the indices are fixed and are the same in all crystals; in the four remaining simple forms they are variable. Triakis-octahedron (three-faced octahedron) (fig. 15). This solid is bounded by twenty-four isosceles triangles, and may be considered as an octahedron with a low triangular pyramid on each of its faces. As the inclinations of the faces may vary there is a series of these forms with the indices {221}, {331}, {3321, &c. or in general {hhk}. Icositetrahedron (fig. 17). Bounded by twenty-four trapezoidal faces, and` hence sometimes called a " trapezohedron." ' The indices are 12111, {3.11}, {322}, &c., or in general {hkk). Analcite, leucite and garnet often crystallize in the simple form {211}. Combinations are shown in figs. 18-20. The plane ABe in fig. 9 is one face (112) of an icositetrahedron; the indices of the remaining faces in this octant being (211) and (121). Tetrakis-hexahedron (four-faced cube) (figs. 21 and 22). Like the triakis-octahedron this solid is also bounded by twenty-four isosceles triangles, but here grouped in fours over the cubic faces. The two figures show how, with different inclinations of the faces, the form may vary, approximating in fig. 21 to the cube and in fig. 22 to the rhombic dodecahedron. The angles over the edges lettered A are different from the angles over the edges lettered C. Each face is parallel to one of the crystallographic axes and intercepts the two FIG. 23.—Combination of others in different lengths; the in- Tetrakis-hexahedron and dices are therefore {210}, 131o}, {320}, Cube. &c., in general ihko}. Fluorspar some- times crystallizes in the simple form {310} ; more usually, however, in combination with the cube (fig. 23). Hexakis-octahedron (fig. 24). Here each face of the octahedron is replaced by six scalene triangles. so that altogether there are J (h2+k2+12) (1'+q2+r2) The angles between faces with the same indices are thus the same in all substances which crystallize in the cubic system: in other systems. the angles vary with the substance and are characteristic of it. forty-eight faces. This is the greatest number of faces possible for any simple form in crystals. The faces are all oblique to the planes and axes of symmetry, and they intercept the three crystallographic axes in different lengths, hence the indices are all unequal, being in general lhkl}, or in particular cases 13211, 14211, 4321, &c. Such a form is known as the " general form " of the class. The interfacial angles over the three edges of each triangle are all different. These forms usually exist only in combination with other cubic forms (for example, fig. 25), but {4211has been observed as a simple form on fluorspar. Several examples of substances which crystallize in this class have been mentioned above under the different forms; many others might be cited—for instance, the metals iron, copper, silver, gold, platinum, lead, mercury, and the non-metallic elements silicon and phosphorus.
End of Article: HOLOSYMMETRIC CLASS (Holohedral (ass, whole)
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SIR CHARLES HOLROYD (1861– )

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